The performance of organometallic perovskite solar cells has rapidly surpassed that of both conventional dye-sensitized and organic photovoltaics. High-power conversion efficiency can be realized in both mesoporous and thin-film device architectures. We address the origin of this success in the context of the materials chemistry and physics of the bulk perovskite as described by electronic structure calculations. In addition to the basic optoelectronic properties essential for an efficient photovoltaic device (spectrally suitable band gap, high optical absorption, low carrier effective masses), the materials are structurally and compositionally flexible. As we show, hybrid perovskites exhibit spontaneous electric polarization; we also suggest ways in which this can be tuned through judicious choice of the organic cation. The presence of ferroelectric domains will result in internal junctions that may aid separation of photoexcited electron and hole pairs, and reduction of recombination through segregation of charge carriers. The combination of high dielectric constant and low effective mass promotes both Wannier-Mott exciton separation and effective ionization of donor and acceptor defects. The photoferroic effect could be exploited in nanostructured films to generate a higher open circuit voltage and may contribute to the current-voltage hysteresis observed in perovskite solar cells.
The performance of organometallic perovskite solar cells has rapidly surpassed that of both conventional dye-sensitized and organic photovoltaics. High-power conversion efficiency can be realized in both mesoporous and thin-film device architectures. We address the origin of this success in the context of the materials chemistry and physics of the bulk perovskite as described by electronic structure calculations. In addition to the basic optoelectronic properties essential for an efficient photovoltaic device (spectrally suitable band gap, high optical absorption, low carrier effective masses), the materials are structurally and compositionally flexible. As we show, hybrid perovskites exhibit spontaneous electric polarization; we also suggest ways in which this can be tuned through judicious choice of the organic cation. The presence of ferroelectric domains will result in internal junctions that may aid separation of photoexcited electron and hole pairs, and reduction of recombination through segregation of charge carriers. The combination of high dielectric constant and low effective mass promotes both Wannier-Mott exciton separation and effective ionization of donor and acceptor defects. The photoferroic effect could be exploited in nanostructured films to generate a higher open circuit voltage and may contribute to the current-voltage hysteresis observed in perovskite solar cells.
The development
of halide pervoskite
solar cells is as rapid as the technology is proving successful.[1−6] Research on these compounds dates to the 1920s.[7] The most widely used hybrid perovskite solar cell material
is methylammonium lead iodide (CH3NH3PbI3 or MAPbI3), where MA is a positively charged organic
cation at the center of a lead iodide cage structure (Figure 1). Initially employed as a light sensitizer in mesoporous
dye cells, these materials also function as an absorber and transport
layer in a solid-state dye cell architecture, and most recently as
the bulk material in a standard planar thin-film solar cell.[8]
Figure 1
Schematic perovskite crystal structure of MAPbI3 (a),
and the possible orientations of molecular dipoles within the lattice
(b). Note that MA has an associated molecular dipole of 2.3 D, a fundamental
difference compared to the spherical cation symmetry in inorganic
perovskites such as CsSnI3.
Here we build upon recent computational
studies[9−16] and calculate the electrostatic cohesion energy, the electronic
band energies, optical transitions, cation molecular polarization
tensors, and energetic barriers for rotation in hybrid lead iodideperovskites. We show how lattice polarization is affected by the polar
organic cation, and how this gives rise to ferroelectric behavior,
which could enhance photovoltaic performance.
Perovskite Structure
The crystal structure adopted
by CaTiO3 (the mineral perovskite) is also found for a
wide range of materials with ABX3 stoichiometry with two
well-studied cases being SrTiO3 and BaTiO3.
Examples of insulating, semiconducting, and superconducting perovskite
structured materials are known; they represent a unique system class
across solid-state chemistry and condensed matter physics. In particular,
they are the archetypal systems for phase transitions with accessible
cubic, tetragonal, orthorhombic, trigonal, and monoclinic polymorphs
depending on the tilting and rotation of the BX6 polyhedra
in the lattice.[17] Reversible phase changes
can be induced by a range of stimuli including electric field, temperature,
and pressure.There have been several reports of structural
characterization for single crystals of MAPbI3 and related
compounds.[18,19] Orthorhombic, tetragonal, and
cubic polymorphs have been identified, analogous to the inorganic
perovskites. Indeed it has been suggested that for MAPbI3 an orthorhombic to tetragonal transition occurs at ∼160 K
with a cubic phase being stable from around 330 K.[19] Disagreement between X-ray and electron diffraction has
been noted, which suggests the presence of nanoscale structural domains.[19] This local disorder is also present in thin-film
samples. The structure of thin-films within mesoporous titania has
been investigated using X-ray scattering,[20] which showed that the majority of the MAPbI3 exists in
a disordered state with a structural coherence length of only 14 Å,
that is, the length of just two PbI3 cages. This behavior
will be explained below in the context of feedback between molecular
and lattice polarization, which is a ferroelectric effect.
Perovskite
Composition
Within the formal stoichiometry
of ABX3, charge balancing can be achieved in a variety
of ways. For metal oxide perovskites (ABO3), the valence
of the two metals must sum to six, that is, I–V–O3, II–IV–O3, and III–III–O3 perovskites are known with common examples being KTaO3, SrTiO3, and GdFeO3. The range of accessible
materials can be extended by partial substitution on the anion sublattice,
for example, in the formation of oxynitride and oxyhalide perovskites.[21] With substitution on the metal sublattice, the
so-called double, triple, and quadruple perovskites are formed,[22] which may offer a route for property optimization
of hybrid compounds.For halide perovskites, the valence of
the two cations must sum to three, so the only viable ternary combination
is I–II-X3, for example, CsSnI3. In hybrid
halide perovskites such as MAPbI3, a divalent inorganic
cation is present with the monovalent metal replaced by an organic
cation of equal charge. In principle, any singly charged molecular
cation could be used, once there is sufficient space to fit it within
the inorganic cage. If the size is too large, then the 3D perovskite
structure is broken, as demonstrated in the series of hybrid structures
with lower dimensionality in the inorganic networks.[15,23−25] For layered structures, the crystal properties become
highly anisotropic.Schematic perovskite crystal structure of MAPbI3 (a),
and the possible orientations of molecular dipoles within the lattice
(b). Note that MA has an associated molecular dipole of 2.3 D, a fundamental
difference compared to the spherical cation symmetry in inorganic
perovskites such as CsSnI3.The stability of ionic and heteropolar crystals, such as
perovskites,
is influenced by the Madelung electrostatic potential. The lattice
energy and site electrostatic potentials is explored for each perovskite
stoichiometry (Table 1).
These are calculated with an Ewald summation (in three dimensions)
of the formal ion charges within the code GULP.[26] For group VI anions, the lattice energy decreases as the
charge imbalance between the A and B sites is removed; a lower charge on the A site
is favored. However, for group VII anions (i.e., halides) the electrostatic
stabilization is notably reduced with a lattice energy of just −29.71
eV/cell and an electrostatic potential on the anion site ca. 50% of
the group VI anions. Because of this weaker, less-confining, potential,
lower ionization potentials (workfunctions) are expected for halideperovskites compared to, for example, metal oxides.[27,28]
Table 1
Electrostatic Lattice Energy and Site
Madelung Potentials for a Range of ABX3 Perovskite Structures
(Cubic Lattice, a = 6.00 Å) Assuming the Formal
Oxidation State of Each Speciesa
stoichiometry
Elattice (eV/cell)
VA (V)
VB (V)
VX (V)
I–V–VI3
–140.48
–8.04
–34.59
16.66
II–IV–VI3
–118.82
–12.93
–29.71
15.49
III–III–VI3
–106.92
–17.81
–24.82
14.33
I–II–VII3
–29.71
–6.46
–14.85
7.75
The hybrid halide
perovskites
are of type I–II–VII3. Calculations are performed
using the code GULP.
From Inorganic to Hybrid Compounds
An important distinction
between inorganic and hybrid perovskites is the change from a spherically
symmetric A site (inorganic) to one of reduced symmetry
(hybrid). The characteristic space groups of perovskite compounds
are formally reduced. For example, the MA cation has the C3 point group and the associated highest-symmetry
perovskite structure will be pseudocubic and not possess the inversion
symmetry of its inorganic analogue. Thus, uncertainty in assigned
average diffraction patterns is not surprising.The presence
of a polar molecule at the center of the perovskite cage also introduces
the possibility of orientational disorder and polarization as drawn
in Figure 1. A typical solid-state dielectric
will exhibit a combination of fast electronic (ε∞) and slow ionic (εionic) polarization, which both
contribute to the macroscopic static dielectric response (ε0 = ε∞ + εionic +
εother). A molecular response (εmolecular) can occur for materials containing molecules with a permanent dipole,
which will likely occur more slowly (due to the moment of inertia
of the molecules, and kinetically limited reordering of domains).
This orientational effect is usually reserved for polar liquids.[29]We have investigated the following energetics
of rotation of three
organic cations within the lead iodide perovskite structure: (i) ammonium,
NH4+ (A); (ii)
methylammonium,CH3NH3+ (MA); and (iii) formamidinium, NH2CHNH2+ (FA).
These were performed using density functional theory (DFT), using
the PBEsol[30] exchange-correlation functional
and the VASP code[31,32] with the setup details previously
reported.[13] Here, we kept the cell lattice
parameters fixed and rotated the cell over the long axis of the molecule,
an equivalent rotation to tumbling the molecule end over end. This
gives us an upper, unrelaxed, limit of the rotation barrier. The resulting
barriers for rotation in the cage are 0.3, 1.3, and 13.9 kJ/mol, respectively.
The value for MA is consistent with observed high rates of rotation
at room temperature from 2H and 14N spectra.[33]The organic cations MA and FA have a large
built-in polarization,
most obviously in the case of methylammonium. To investigate this
we calculate the polarization tensor in vacuum with the GAUSSIAN[34] package on singly charged cations. We find that
the molecular polarization tensor is dominated by a dipole contribution.
The dipoles, in Debye, for B3LYP/6-31G* (CCSD/cc-pVQZ) calculations
are (i) A, 0.0 (0.0); (ii) MA, 2.29 (2.18); and (iii) FA, 0.21 (0.16).
An obvious route to increasing the strength of this dipole is successive
fluorination of the methyl in methylammonium. We calculate the dipole
increase from methylammonium (2.29 D) to mono-, bi- and trifluorination
to be 5.35, 6.08, and 6.58 D, respectively (B3LYP/6-31G*). These permanent
dipoles will interact with an external electric field and with each
other.In the hybrid perovskite, the cations are surrounded
by a polarizable
medium (the perovskite cage), whereas our dipole calculations are
in the gas phase. As a first approximation, we therefore repeat these
calculations with the polarizable continuum model (PCM) with a choice
of solvent (ethanol, ε0 = 24.852) that matches our
calculated dielectric constant for the bulk material and is a suitably
bulky solvent that it should have a comparable cavity volume to the
pore in the perovskite cage. We use the gas phase geometries. The
dipoles in Debye for B3LYP/6-31G* PCM calculations with ethanol are
(i) A, 0.0; (ii) MA, 2.65; (iii) FA, 0.24; (iv) MA-F3, 7.19. A more
careful calculation would require a better model for the cavity; however
these data do show that only a small deviation from the gas phase
values occur, which suggests that the permanent dipole moment of these
molecules is robust to the local polarization environment.The hybrid halideperovskites
are of type I–II–VII3. Calculations are performed
using the code GULP.A significant
increase in dipole moment (from 2.3 to 6.6 D, by
a vacuum calculation with B3LYP/6-31G*) is achieved through increasing
the degree of methyl-fluorination.Hybrid halide perovskite solar cells have a typical active
region
thickness of 1 μm and a built in voltage of 1 V, resulting in
an electric field of ca. 1 × 106 Vm–1. The dipole potential energy is U = −pE, and so the energy change in going from aligned to antialigned
with the electric field is 2pE or 4 × 10–5 eV D–1. The interaction energy
of 9 × 10–2 meV for MA is small compared to
the thermal energy, and so weak macroscopic ordering of the cations
as a result of the internal field of the solar cell is expected, but
more careful quantification is required to understand the field interactions
with domains.The interaction energy of two point dipoles, going
from parallel
ferroelectric to antiferroelectric alignment, isIn applying this to nearest-neighbor
cation dipoles within the
perovskite structure, we are making two approximations. The first
is the point dipole approximation. Our molecules are too close for
this to be correct and the origin of the molecular dipole is likely
to move within the perovskite cage as the cation rotates. The second
is in assuming the vacuum dielectric constant. There will be electron
density shielding the region of space between these two cations, but
the cations face each other through a relatively open face of the
perovskite structure; the upper limit of the screening is the macroscopic
static dielectric constant (ε0 = 25.7 for MAPbI3)[13] that should be valid over longer
distances.Due to the many unknowns in the location and dynamic
behavior of
the cation and the difficulty in fully treating the interaction of
the molecular charge density with the periodic electronic structure
of the perovskite, we present these energies as a first approximation.
These energies can be used to parametrize a classical Hamiltonian
for the interaction of the rotating dipoles and as activation energies
for use in looking for order–disorder transitions experimentally.Considering a cubic perovskite structure with 6.29 Å between
nearest neighbors, the parallel ferroelectric alignment energy of
methylammonium is 48 meV. Because of the p2 dependence on the dipole moment while keeping methylammonium lattice
parameters, this energy is much smaller than thermal energy for FA,
0.3 meV; zero for A; and much greater for fluorinated MA, 436 meV.Systematic variation of the organic cation (such as by fluorination)
and studying the electrical properties of the resulting devices would
offer direct evidence of the molecular dipole derived contribution
to the operation of hybrid halide perovskite solar cells. Polarization
of the inorganic perovskite cage will be discussed separately below.
Electronic Structure
For MAPbI3 and related
materials, the upper valence band is predominately composed of I 5p
orbitals, while the conduction band is formed of Pb 6p.[13,14] There is hybridization between the filled Pb 6s band with I 5p that
result in antibonding states at the top of the valence band (analogous
to p–d coupling in II–VI semiconductors). Electron and
hole conduction therefore occurs along distinct pathways at the R point of the first Brillouin zone.[14] Both Pb and I are heavy ions, and as such both the valence
and conduction bands contain considerable relativistic effects, that
is, for a quantitative treatment of the electronic band structure
spin–orbit coupling must be included.[14] The band gap predicted by a relativistic self-consistent quasiparticle
GW method is 1.67 eV, which is in good agreement with the measured
value of 1.61 eV from room temperature photoluminescence (PL).[35]Lead is commonly used in ferroelectric
and multiferroic materials as its lone pair of electrons is a driving
force for structural distortions.[36,37] Note that
the multivalency of Pb (and Sn for stannous halides) will also be
important for the defect chemistry. While present as divalent cations
in these structures (s2p0), a higher tetravalent
oxidation state is also accessible (s0p0). Self-oxidation
could facilitate the generation of electrons (n-type doping; PbII → PbIV + 2e–) or in
the trapping of holes (p-type compensation; PbII + 2h+ → PbIV). The thermodynamics of these processes
merit further investigation.For all cases investigated, the
organic cation acts as a charge
compensating center but does not participate in the frontier electronic
band structure.[13,15] Occupied molecular states are
found well below the top of the valence band and empty molecular states
found well above the bottom of the conduction band. The choice of
organic moiety does influence the lattice constant and, therefore,
will change the electronic structure indirectly, in a similar manner
to the application of hydrostatic pressure.Unusually, the band
gaps of hybrid perovskites have been reported
to increase with increasing cell volume (decreasing pressure),[15] which is opposite to the behavior of most semiconductors.[38] Indeed the calculated band gap deformation potentialfor MAPbI3 is positive (αVR = 2.45 eV). As
the fundamental band gap is determined at the boundary of the Brillouin
zone (R), the out-of-phase band-edge states are stabilized
as the lattice expands. Similar behavior is observed for Pb chalcogenides.[39] The deformation of the gap at the Γ point
is negative (αV = −1.08 eV), following standard
expectation. Measurements of temperature dependent PL indicate a decrease
in band gap with decreasing temperature (lattice contraction) to ∼1.55
eV at 150 K, which is at the onset of a phase change.[35]The implication of the deformation potential is that
for smaller
molecular cations, lower band gaps should be observed. Indeed, the
smallest possible counterion is a proton (H+) to form HPbI3, which results in a calculated lattice parameter of 6.05
Å and an associated band gap of less than 0.3 eV. In contrast,
the band gap changes on halide substitution are influenced more by
the electronic states of the anion, that is, from Cl to Br to I the
valence band composition changes from 3p to 4p to 5p with a monotonic
decrease in electron binding energy (lower ionization potential).
The substitution of Br by I in FAPbX3 has been shown to
decrease the band gap from 2.23 to 1.48 eV.[40]The effective masses of both carriers are k-dependent,
as the result of nonparabolic energy bands near the extremal points,
as confirmed by self-consistent GW calculations.[14] These calculations have also shown that relativistic renormalization
of the band gap is of a similar magnitude to the band gap itself;
these materials are far removed from conventional semiconductors such
as Si. Close to the band extrema the carriers are light with mh* and me* of approximately 0.12 m0 and
0.15 m0, respectively.[41]As a result of the high dielectric constant, the
associated Wannier-Mott
exciton radius (within effective mass theory, that is, a0 = ε0/m in au)[42] is large (204
Å) with a binding energy (Eb = 1/(2ε0a0)) of 0.7 meV. It is clear that
excitons will not play a significant role in the photovoltaic device
physics. Indeed, magnetoabsorption measurements at 4.2 K suggested
an exciton radius of 28 Å and a binding energy of 37 meV in the
low-temperature low-symmetry phase of single-crystal MAPbI3.[43]The valence band energy (ionization potential)
of MAPbI3 is 5.7 eV below the vacuum level (Figure 3). The computed bulk ionization potential and electron
affinity of
5.7 and 4.1 eV are consistent with the use of TiO2 (electron
acceptor) and Au (gold acceptor) in photovoltaic devices.[8] This ionization potential is comparable to thin-film
solar cell absorbers such as Cu2ZnSnS4,[44] which implies that other device configurations,
for example, a Mo back-contact (to replace Au) and a CdS buffer layer
(to replace TiO2), are possible. In contrast, the valence
band of Si is significantly higher in energy.
Figure 3
Valence band ionization potentials of MAPbI3 with respect
to the vacuum level. Calculations were performed on the nonpolar (110)
surface with slab thickness of 25 Å and a vacuum thickness of
15 Å. The Kohn–Sham eigenvalues (PBEsol) are corrected
by the bulk quasi-particle energies (ΔE = 0.2
eV). Values for the energetically similar inorganic thin-film absorber
Cu2ZnSnS4[45] and Si[46] are shown for comparison.
Carriers, Defects and Decomposition
The bulk electronic
structure also has implications for carrier concentrations. These
materials are intrinsic semiconductors with initial reports of relatively
high doping densities, for example, above 1019 cm–3 in MASnI3.[47] Unlike traditional
inorganic absorber materials where defect formation can be controlled
thermodynamically, the solution processing of these materials at low
temperatures is more likely to be kinetically controlled with defects
in the lattice (e.g., cages with missing MA cations) being a product
of the crystallization process. Initial computations suggest that
the low energy defects all exhibit resonant or shallow impurity bands.[16]Valence band ionization potentials of MAPbI3 with respect
to the vacuum level. Calculations were performed on the nonpolar (110)
surface with slab thickness of 25 Å and a vacuum thickness of
15 Å. The Kohn–Sham eigenvalues (PBEsol) are corrected
by the bulk quasi-particle energies (ΔE = 0.2
eV). Values for the energetically similar inorganic thin-film absorber
Cu2ZnSnS4[45] and Si[46] are shown for comparison.The Mott criterion (na0 = 0.26)[48] based on the calculated band structure parameters, predicts a transition
to a degenerate semiconductor could happen from carrier concentrations
(n) as low as 1016cm–3. Note that this is a lower estimate
that will be increased by both the nonparabolic nature of the band
edges and fluctuations in the local elecrostatic potentials due to
structural inhomogeneity.There are a number of potential routes
for the control of carrier
concentrations (doping). First, a mixture of charged and neutral counter-cations
(e.g., NH4+ and NH3) would result in an electron deficiency and hence
p-type doping. Conversely, the inorganic cage could be altered by
partial substitution of Pb by a trivalent cation would result in an
electron excess and hence n-type doping. Tl and Bi are two obvious
candidates due to their similar size.There are reports of hybrid
perovskites reacting with Lewis bases
with the most notable being irreversible degradation in the presence
of H2O and temporary bleaching in the presence of ammonia.[49] There are several plausible mechanisms by which
this decomposition may occur. We propose the simple acid–base
reaction shown in Figure 4. In the case of
water exposure, a single water molecule is sufficient to degrade the
material; however, an excess of water is required to dissolve the
HI and CH3NH2 byproducts. As a result, a closed
system with trace amounts of H2O will result in partial
decomposition of the hybrid perovskite until either (i) the HI has
saturated the H2O or (ii) the vapor pressure of CH3NH2 has reached equilibrium. In the presence of
sufficient water the material degrades entirely to form PbI2.
Figure 4
Possible decomposition pathway of hybrid halide perovskites in
the presence of water. A water molecule, a, is required
to initiate the process with the decomposition being driven by the
phase changes of both hydrogen iodide, (b, soluble in
water) and the methylammonia (c, volatile and soluble
in water). This pathway results in the formation of a yellow solid,
which corresponds the experimentally observed PbI2, d.
Possible decomposition pathway of hybrid halide perovskites in
the presence of water. A water molecule, a, is required
to initiate the process with the decomposition being driven by the
phase changes of both hydrogen iodide, (b, soluble in
water) and the methylammonia (c, volatile and soluble
in water). This pathway results in the formation of a yellow solid,
which corresponds the experimentally observed PbI2, d.The proposed mechanism
for reversible perovskite bleaching is similar
to that of water decomposition, where a reaction analogous to Figure 4 may occur. In this case, the ionic salt (and strong
acid) HI, would form a separate ionic salt with NH3. This
Grotthuss mechanism[50] should cause a concerted
proton transfer throughout the material resulting in three thermally
reversible outcomes: (i) the methylammonia evaporates, resulting in
the inclusion of NH4 as the organic ion in the perovskite,
with the simultaneous production of HI; (ii) the system degrades to
form HI, PbI2, and volatile organics; and (iii) the CH3NH3+/CH3NH2–NH3/NH4+ reaction occurs
on the surface causing the material to form the neutral CH3NH2. This acid–base reaction is reversible and
ammonia is more volatile than the heavier methylammonia (which may
be trapped within the material), resulting in transient bleaching.To our knowledge, there has been no reports of hybrid perovskites
incorporating aprotic organic ions (such as tetramethylammonium, (CH3)4N+). Such a material would not be
capable of the reaction mechanism depicted in Figure 4 and so may be more chemically stable. The built-in molecular
dipole, which could be important for the performance of these materials
in a solar cell, could be achieved by selective flourination.We speculate that decomposition or reversible bleaching should
be observed in the presence of any small Lewis acid with a protic
hybrid perovskite, and such an experimental study would help understanding
the degradation pathways of hybrid perovskite solar cells.
Spontaneous
Electric Polarization
Most inorganic perovskites
display spontaneous electric polarization, arising from the breaking
of crystal centro-symmetry, as a result of the B cation
moving away from the center of the BX6 octahedron.[17] The phenomenon is particularly
pronounced in hybrid halide perovskites, where the asymmetry of the
organic cation ensures the absence of an inversion center in the structure.The magnitude of the bulk polarization has been probed using Berry
phase calculations within the modern theory of polarization.[51,52] The calculated values (PBEsol functional) are presented in Table 2. For MAPbI3, the electronic polarization
of 38 μC/cm2 is comparable to ferroelectric oxide
perovskites (e.g., ca. 30 μC/cm2 in KNbO3[53]). Indeed, the application of ferroelectric
oxides to photovoltaics has been recently demonstrated.[54]
Table 2
Calculated
Properties of Four Hybrid
Lead Halide Perovskites from Density Functional Theorya
Cation
D
a
ΔP
Erot
Edip
NH4
0.00
6.21
8
0.3
0.00
CH3NH3
2.29
6.29
38
1.3
4.60
CF3NH3
6.58
6.35
48
21.4
42.00
NH2CHNH2
0.21
6.34
63
13.9
0.03
The molecular dipole (D) is given in Debye, calculated
by vacuum B3LYP/6-31G*
in GAUSSIAN. The pseudo-cubic lattice constant (a = (V)1/3) in Å; the lattice electronic
polarisation (ΔP) in μC/cm2; and the rotation barrier (Erot) in
kJ/mol, calculated by PBESol in VASP. The nearest-neighbour dipole
interaction (Edip) in kJ/mol is estimated
from a point dipole calculation.
The strong polarization of the lattice
has two potential advantages
for photovoltaic operation: (i) enhanced charge separation and concomitant
improved carrier lifetimes;[55] (ii) open
circuit voltages above the band gap of the material.[54] Both effects are linked to the internal electric field,
which results as a consequence of lattice polarization. The mechanisms
are shown schematically in Figure 5.
Figure 5
Schematic
of the 1D built-in potential (upper panels) and associated
2D electron and hole separation pathways (lower panels) in (a,d) a
macroscopic p–n junction; (b,e) a single domain ferroelectric
thin-film; (c,f) a multidomain ferroelectric thin-film. In the multidomain
ferroelectric, which we propose for hybrid perovskites, electrons
will move along minima in the potential, while holes will move along
maxima (i.e., antiphase boundaries).
Traditional semiconductor photovoltaic devices separate charge
carriers at p–n junctions (Figure 5a).
A ferroelectric domain with its built-in electric field (Figure 5b) acts to separate the exciton generated by photoabsorption
in effect acting as a p–n junction. A standard planar p–n
junction is on the order of micrometers and separated charge carriers
must diffuse through the junction to reach their respective electrodes;
during this diffusion process carriers may encounter one another and
recombine. The size of ferroelectric domains is smaller on the nanometer
scale (several cages for the hybrid perovskites). The probability
of carrier recombination within a domain is therefore reduced with
respect to a traditional heterojunction.The carriers in the
ferroelectric material can diffuse to domain
boundaries, where there is a buildup of carriers of a given type (Figure 5c) along peaks and troughs in the electric potential
generated by local dipole order. The carriers may then diffuse along
these “ferroelectric highways” toward the electrodes,
unimpeded by carriers of the opposite charge; essentially we have
an intrinsic semiconductor region where local hole and electron segregation
reduces recombination. We propose this as the origin of exceptionally
long carrier diffusion lengths[56,57] despite local structural
disorder. The carrier density of these ferroelectric boundaries as
well as the domain orientation will be influenced by the applied voltage
and hence give rise to hysteresis, or spurious fluctations, in electrical
measurements.The contribution of these photoferroic effects
could be assessed
and controlled by modification of the counterion. The molecular dipole
can be tuned with the simple example discussed earlier being the incorporation
of more electronegative species on one side of the MA cation (Figure 2). Even for APbI3, where there is no
molecular dipole, the lattice is weakly polarized (8 μC/cm2) and this effect would likely be enhanced toward lower symmetry
interfaces and grain boundaries. Notably, the largest degree of polarization
is observed for FAPbI3 (63 μC/cm2), which
is not the most polar cation, but its larger size induces a polar
deformation of the PbI3 cage.
Figure 2
A significant
increase in dipole moment (from 2.3 to 6.6 D, by
a vacuum calculation with B3LYP/6-31G*) is achieved through increasing
the degree of methyl-fluorination.
The molecular dipole (D) is given in Debye, calculated
by vacuum B3LYP/6-31G*
in GAUSSIAN. The pseudo-cubic lattice constant (a = (V)1/3) in Å; the lattice electronic
polarisation (ΔP) in μC/cm2; and the rotation barrier (Erot) in
kJ/mol, calculated by PBESol in VASP. The nearest-neighbour dipole
interaction (Edip) in kJ/mol is estimated
from a point dipole calculation.Schematic
of the 1D built-in potential (upper panels) and associated
2D electron and hole separation pathways (lower panels) in (a,d) a
macroscopic p–n junction; (b,e) a single domain ferroelectric
thin-film; (c,f) a multidomain ferroelectric thin-film. In the multidomain
ferroelectric, which we propose for hybrid perovskites, electrons
will move along minima in the potential, while holes will move along
maxima (i.e., antiphase boundaries).It is interesting to note that the “ferroelectric
highways”
are distinct but similar to the proposed mechanism for carrier separation
in thin-film CuInSe2 solar cells, where Cu-rich and Cu-poor
domains (ordered defect complexes) have been linked to internal homojunctions
that facilitate efficient charge carrier separation and reduced carrier
recombination.[58,59]In summary, we have provided
insights into the key materials properties
of organometallic perovskites that contribute to their photovoltaic
performance. Further investigations are required to assess the mechanisms
proposed including the role of ferroelectric domains and the small
exciton binding energies. Opportunities have been discussed for rational
modification of material characteristics through modifying the organic
cation. In particular, we suggest manipulating the dipole moment (to
affect ferroelectric behavior and dielectric constant), cation size
(to manipulate band gap and ferroelectric behavior) and to move to
an aprotic cation (to avoid a degradation pathway). A lead free material
with high performance and reduced degradation would represent a major
step forward for this technology. We hope that the description of
the atomistic origin of favorable material characteristics exhibited
by MAPI3 may offer some guidance for the design of improved
organometallic perovskites.
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